Waterloo Bridge (1940) [Myra Lester]: Commits suicide by walking into traffic on the bridge; we hear tires screech as she walks out of frame, followed by a shot of a crowd gathered around her body (though we can't see her through the crowd). (Thanks to Scott)

Anna Karenina(1948) [Anna Karenina]: Commits suicide by throwing herself under the wheels of a train. (I haven't seen this version, but I'm familiar with the story.)

The Roman Spring of Mrs. Stone(The Widow and the Gigolo) (1961) [Karen Stone]: Possibly killed (off-screen) by Jeremy Spenser after she lets him into her apartment; the movie ends as he enters and approaches her, but it's implied that she will be killed. (Jeremy's nameless character is even sometimes interpreted as a symbolic personification of death.)